Mathematicians have long searched for an ‘einstein’ shape – not referring to the physicist Albert Einstein, but from the German ‘one stone’ – that can cover an infinite surface in a pattern that does not repeat. The first einstein to be identified was nicknamed “the hat” and is a 13-sided polygon made up of smaller kite-like shapes merged together. By combining an infinite number of “hats” and their mirror images, an endless non-repeating array can be formed.

Only a few months after the discovery of “the hat,” another einstein tile was found. This time, the shape could be lain out in a non-repeating pattern even without the use of its mirror image. In the absence of the shape’s reflection, it was nicknamed the “vampire einstein.” When mathematicians guessed what the first identified einsteins would look like, they had no idea they would take such simple forms.

What does this mean for the real world? Knowing that simple shapes could be aperiodic (non-repeating) could have major implications for materials science, a field of engineering that identifies materials used for construction and manufacturing. Chemist Daniel Schectman was awarded the Nobel Prize for his 1982 discovery of quasicrystals: crystals whose atoms are packed in a non-repeating pattern. The non-repeating nature of quasicrystals makes them extremely strong but also poor conductors of heat. They have since been used in blends of steel for making surgical instruments and are being considered as insulators in engines. Time will tell how the discovery of einstein shapes may affect material science in the future.